What you see here is a magic square, much like the addition
and subtraction squares you may have used as a child.
These magic squares are even more talented, as they
all follow the rules of the card game SET®. To learn how to make
one with ease, read on.
SET® cards contain four properties: color, shape,
number of objects, and shading. The rules state for each
property, they must all be equal, or all different. For example, if
we look at the top row of the square, we see three different colors,
three different shapes, three different numbers, and three different
types of shading within the objects. Need more examples? Any line on
the magic square yields a set.
Constructing a magic square may seem complex at first glance, but in
reality anyone can make one by following this simple process:
Choose any three cards that are not a set. (It will work with
a set but the square becomes redundant) For example, we will choose
|Now place these three cards in the #1, #3, and #5 positions
in the magic square.
Using our powers of deduction, we can conclude that in order
to create a set in the first row, the #2 card needs to have a different
color, different shape, same number, and same shading as the #1
and #3 cards. That leaves us with a solid purple oval. The rest
of the square can be completed in the same way, giving us the following
A few examples will convince you that this method works. Not only
does the magic square work but it can be theoretically proven through
a mathematical model. This model makes an easy
proof of the magic square, as well as answer any questions about how
Proof of the Magic Square
| More Math Tricks